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Re: Converting the integral of a sum into a sum of integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109147] Re: Converting the integral of a sum into a sum of integrals
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Mon, 19 Apr 2010 04:11:37 -0400 (EDT)
  • References: <201004110831.EAA06714@smc.vnet.net> <hputps$lhj$1@smc.vnet.net>

Kurt TeKolste schrieb:
> If I ask Mathematica to perform an indefinite integrate on a symbolic
> summation (with terms of the form a_i x^i),
> 
> Integrate[Sum[Times[Power[x,i],Subscript[a,i]],{i,0,k}],
> 
> it does nothing.  If I try to tell it that summation and integration
> commute by applying the rule:
> 
> Integrate[Sum[term_,range_],variable_]->
> Sum[Integrate[term_,variable_],range_]
> 
> I get a strange result equivalent to
> 
> term * range

meaning that Integrate does not see term dependent on variable

> 
> or, in this case,
> 
> Times[Power[x,i],Subscript[a,i]] * {i,0,k}
> or
> {i a_i x^i, 0, k a_i x^i}
> 
> Any ideas as to what's going on?
> 
> (BTW:
> 
> 1)  If you use rules to extract each of term, range, and variable and
> then take Sum[Integral[...],...] the correct answer is returned.
> 
> 2)  if you use a rule that changes Sum to Power, i.e.
> 
> Integrate[Sum[term_,range_],variable_] ->
> Product[Integrate[term_,variable_],range_]
> 
> you get exponents
> 
> term^(range - 1)
> 
> Odd...
> )
> 
> ekt
> 


Use rules that hold its pattern form unevaluated. HoldPattern preserves 
execution of the first argument of RuleDelayed at any stage of the 
defining or execution process.

Using RuleDelayed (:> )instead of Rule (->) delays evaluation of its 
second argument to the time of applying the rule in a Replace (/.)

-- 

Roland Franzius
rule = HoldPattern[Integrate[Sum[expression_,j_],x_] :> 
Sum[Integrate[expression,x],j]


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